A body of mass 0.5 kg is thrown vertically upwards with a speed of 10 m/s. Determine:
a.The initial kinetic energy of the body
b.The gain in potential energy when the body has reached its maximum height
c.The maximum height reached above the starting position
a. KE = 0.5m*V^2.
KE = 0.5*0.5 * 10^2 = 25 Joules.
b. PE = Loss in KE = 25 Joules.
c. hmax = (V^2-Vo^2)/2g.
hmax = (0-(10^2)) / -19.6 = 5.10 m.
To solve these questions, we need to consider the principles of energy and motion. Let's break down each part step by step:
a. The initial kinetic energy of the body:
The formula to calculate the kinetic energy (KE) of an object is:
KE = (1/2) * mass * velocity^2
Given:
Mass (m) = 0.5 kg
Velocity (v) = 10 m/s
Substituting these values into the formula, we get:
KE = (1/2) * 0.5 kg * (10 m/s)^2
= 0.5 * 0.5 kg * 100 m^2/s^2
= 25 Joules
Therefore, the initial kinetic energy of the body is 25 Joules.
b. The gain in potential energy when the body has reached its maximum height:
The potential energy (PE) of an object is given by the formula:
PE = mass * acceleration due to gravity * height
Since the body reaches its maximum height, its final kinetic energy is zero, meaning all its initial kinetic energy is converted into potential energy.
Also, at the highest point, the body comes to rest, so its final velocity is zero.
Given:
Mass (m) = 0.5 kg
Acceleration due to gravity (g) = 9.8 m/s^2
Velocity (v) = 0 m/s (final velocity)
Using the principle of conservation of energy, we can equate the initial kinetic energy (KE) to the final potential energy (PE):
KE = PE
(1/2) * mass * velocity^2 = mass * acceleration due to gravity * height
(1/2) * 0.5 kg * (10 m/s)^2 = 0.5 kg * 9.8 m/s^2 * height
Simplifying,
25 Joules = 4.9 Joules/m * height
Therefore, the gain in potential energy (PE) when the body has reached its maximum height is 25 Joules.
c. The maximum height reached above the starting position:
Now, we can rearrange the equation from part b to solve for the height:
height = (25 Joules) / (0.5 kg * 9.8 m/s^2)
= 25 J / 4.9 Joules/m
≈ 5.1 meters
So, the maximum height reached above the starting position is approximately 5.1 meters.